On some invariant ideals, and on extension of differentiations to seminormalization

Abstract

AbstractLet A be a noetherian integral domain, D=(1,D1,…,Di…) be a differentation of A, and B be a ring such that A⊂B⊂Ā. In the paper we mainly prove (whenever Ā is finite over A): (a) if α is the conductor of A in B, then A√α is D-invariant. (b) D extends to the seminormalization +A of A in Ā